Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1935333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 10x^{2} + 13x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.43444\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.43444 | 0.828175 | 0.414087 | − | 0.910237i | \(-0.364101\pi\) | ||||
0.414087 | + | 0.910237i | \(0.364101\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.63444 | −0.730942 | −0.365471 | − | 0.930823i | \(-0.619092\pi\) | ||||
−0.365471 | + | 0.930823i | \(0.619092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.942381 | −0.314127 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.97894 | 1.19969 | 0.599847 | − | 0.800115i | \(-0.295228\pi\) | ||||
0.599847 | + | 0.800115i | \(0.295228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.47100 | 0.685331 | 0.342665 | − | 0.939457i | \(-0.388670\pi\) | ||||
0.342665 | + | 0.939457i | \(0.388670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34450 | −0.605347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.38106 | −1.06256 | −0.531281 | − | 0.847196i | \(-0.678289\pi\) | ||||
−0.531281 | + | 0.847196i | \(0.678289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0365556 | 0.00838643 | 0.00419321 | − | 0.999991i | \(-0.498665\pi\) | ||||
0.00419321 | + | 0.999991i | \(0.498665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.565560 | 0.117927 | 0.0589637 | − | 0.998260i | \(-0.481220\pi\) | ||||
0.0589637 | + | 0.998260i | \(0.481220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.32862 | −0.465724 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65511 | −1.08833 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.34450 | 0.435363 | 0.217681 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217681 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.365564 | −0.0656573 | −0.0328286 | − | 0.999461i | \(-0.510452\pi\) | ||||
−0.0328286 | + | 0.999461i | \(0.510452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.70755 | 0.993556 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.76093 | −0.289495 | −0.144748 | − | 0.989469i | \(-0.546237\pi\) | ||||
−0.144748 | + | 0.989469i | \(0.546237\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.54450 | 0.567574 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.38106 | −0.363108 | −0.181554 | − | 0.983381i | \(-0.558113\pi\) | ||||
−0.181554 | + | 0.983381i | \(0.558113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.54026 | 0.229609 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.3188 | −1.94275 | −0.971374 | − | 0.237554i | \(-0.923654\pi\) | ||||
−0.971374 | + | 0.237554i | \(0.923654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.28436 | −0.879987 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.63444 | −0.224507 | −0.112254 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112254 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.50332 | −0.876907 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0524368 | 0.00694543 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.70755 | 0.743059 | 0.371530 | − | 0.928421i | \(-0.378833\pi\) | ||||
0.371530 | + | 0.928421i | \(0.378833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6362 | −1.61790 | −0.808948 | − | 0.587880i | \(-0.799963\pi\) | ||||
−0.808948 | + | 0.587880i | \(0.799963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.03868 | −0.500937 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.1764 | 1.73193 | 0.865964 | − | 0.500107i | \(-0.166706\pi\) | ||||
0.865964 | + | 0.500107i | \(0.166706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.811262 | 0.0976644 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.10081 | 0.842711 | 0.421355 | − | 0.906896i | \(-0.361554\pi\) | ||||
0.421355 | + | 0.906896i | \(0.361554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.24781 | 0.614209 | 0.307105 | − | 0.951676i | \(-0.400640\pi\) | ||||
0.307105 | + | 0.951676i | \(0.400640\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.34027 | −0.385701 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.14700 | 0.241556 | 0.120778 | − | 0.992680i | \(-0.461461\pi\) | ||||
0.120778 | + | 0.992680i | \(0.461461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.28478 | −0.587197 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1008 | −1.43800 | −0.719000 | − | 0.695010i | \(-0.755400\pi\) | ||||
−0.719000 | + | 0.695010i | \(0.755400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.16056 | 0.776671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.36305 | 0.360556 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.33073 | 0.141057 | 0.0705283 | − | 0.997510i | \(-0.477531\pi\) | ||||
0.0705283 | + | 0.997510i | \(0.477531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.524380 | −0.0543757 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0597478 | −0.00612999 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.30332 | −0.640005 | −0.320003 | − | 0.947417i | \(-0.603684\pi\) | ||||
−0.320003 | + | 0.947417i | \(0.603684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.74967 | −0.376856 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0637 | 1.00137 | 0.500687 | − | 0.865628i | \(-0.333081\pi\) | ||||
0.500687 | + | 0.865628i | \(0.333081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1713 | −1.69193 | −0.845967 | − | 0.533235i | \(-0.820976\pi\) | ||||
−0.845967 | + | 0.533235i | \(0.820976\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.45088 | 0.526956 | 0.263478 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263478 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.55788 | −0.723914 | −0.361957 | − | 0.932195i | \(-0.617891\pi\) | ||||
−0.361957 | + | 0.932195i | \(0.617891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.52595 | −0.239753 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.75643 | −0.165231 | −0.0826154 | − | 0.996582i | \(-0.526327\pi\) | ||||
−0.0826154 | + | 0.996582i | \(0.526327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.924371 | −0.0861980 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.32862 | −0.215281 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.83194 | 0.439267 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.43444 | −0.129339 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9782 | 1.07136 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.12398 | 0.277208 | 0.138604 | − | 0.990348i | \(-0.455738\pi\) | ||||
0.138604 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.41548 | −0.300717 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.15630 | −0.799989 | −0.399995 | − | 0.916517i | \(-0.630988\pi\) | ||||
−0.399995 | + | 0.916517i | \(0.630988\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.24291 | 0.795503 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.9966 | −1.53755 | −0.768775 | − | 0.639520i | \(-0.779133\pi\) | ||||
−0.768775 | + | 0.639520i | \(0.779133\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9527 | −1.09863 | −0.549316 | − | 0.835614i | \(-0.685112\pi\) | ||||
−0.549316 | + | 0.835614i | \(0.685112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.1050 | −1.60893 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.83194 | 0.822188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.83194 | −0.318225 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2999 | 1.25341 | 0.626707 | − | 0.779255i | \(-0.284402\pi\) | ||||
0.626707 | + | 0.779255i | \(0.284402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4007 | −1.66018 | −0.830091 | − | 0.557628i | \(-0.811712\pi\) | ||||
−0.830091 | + | 0.557628i | \(0.811712\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.12862 | 0.333779 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.597491 | 0.0479916 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1081 | 0.806716 | 0.403358 | − | 0.915042i | \(-0.367843\pi\) | ||||
0.403358 | + | 0.915042i | \(0.367843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.34450 | −0.185931 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.14940 | −0.168354 | −0.0841769 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841769 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.32862 | −0.726232 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.36092 | 0.105311 | 0.0526555 | − | 0.998613i | \(-0.483231\pi\) | ||||
0.0526555 | + | 0.998613i | \(0.483231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.89418 | −0.530321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0344493 | −0.00263440 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1485 | 0.771572 | 0.385786 | − | 0.922588i | \(-0.373930\pi\) | ||||
0.385786 | + | 0.922588i | \(0.373930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.18714 | 0.615383 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.18806 | −0.537261 | −0.268630 | − | 0.963243i | \(-0.586571\pi\) | ||||
−0.268630 | + | 0.963243i | \(0.586571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.94623 | −0.590638 | −0.295319 | − | 0.955399i | \(-0.595426\pi\) | ||||
−0.295319 | + | 0.955399i | \(0.595426\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.1258 | −1.33990 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.87813 | 0.211604 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.4319 | −1.27475 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.2376 | −1.60906 | −0.804529 | − | 0.593913i | \(-0.797582\pi\) | ||||
−0.804529 | + | 0.593913i | \(0.797582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.92940 | 0.642752 | 0.321376 | − | 0.946952i | \(-0.395855\pi\) | ||||
0.321376 | + | 0.946952i | \(0.395855\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.79325 | −0.414863 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.70043 | 0.691127 | 0.345563 | − | 0.938395i | \(-0.387688\pi\) | ||||
0.345563 | + | 0.938395i | \(0.387688\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.80451 | 0.695023 | 0.347512 | − | 0.937676i | \(-0.387027\pi\) | ||||
0.347512 | + | 0.937676i | \(0.387027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.3353 | 1.43434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.63444 | 0.114154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.532973 | −0.0370442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.145452 | 0.0100612 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3395 | −1.12486 | −0.562428 | − | 0.826847i | \(-0.690132\pi\) | ||||
−0.562428 | + | 0.826847i | \(0.690132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1857 | 0.697912 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.89168 | 0.265411 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.52767 | 0.508673 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8256 | −0.728207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9703 | 1.13642 | 0.568208 | − | 0.822885i | \(-0.307637\pi\) | ||||
0.568208 | + | 0.822885i | \(0.307637\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.19445 | 0.146296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.9782 | 1.59149 | 0.795743 | − | 0.605634i | \(-0.207081\pi\) | ||||
0.795743 | + | 0.605634i | \(0.207081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.07735 | 0.335520 | 0.167760 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167760 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2293 | −0.801166 | −0.400583 | − | 0.916261i | \(-0.631192\pi\) | ||||
−0.400583 | + | 0.916261i | \(0.631192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.7687 | 1.42004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.07974 | 0.200051 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.0981 | −1.10599 | −0.552993 | − | 0.833186i | \(-0.686515\pi\) | ||||
−0.552993 | + | 0.833186i | \(0.686515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.61085 | −0.425843 | −0.212921 | − | 0.977069i | \(-0.568298\pi\) | ||||
−0.212921 | + | 0.977069i | \(0.568298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.38464 | 0.602025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0903287 | 0.00574748 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.7923 | −1.19092 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.5209 | −0.916553 | −0.458277 | − | 0.888810i | \(-0.651533\pi\) | ||||
−0.458277 | + | 0.888810i | \(0.651533\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.25033 | 0.141477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.2714 | 0.643219 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.78315 | 0.235987 | 0.117993 | − | 0.993014i | \(-0.462354\pi\) | ||||
0.117993 | + | 0.993014i | \(0.462354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.20941 | −0.136759 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.5159 | −1.88169 | −0.940846 | − | 0.338836i | \(-0.889967\pi\) | ||||
−0.940846 | + | 0.338836i | \(0.889967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67138 | 0.164102 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.90885 | 0.116820 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.04624 | 0.246704 | 0.123352 | − | 0.992363i | \(-0.460636\pi\) | ||||
0.123352 | + | 0.992363i | \(0.460636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.130195 | 0.00790876 | 0.00395438 | − | 0.999992i | \(-0.498741\pi\) | ||||
0.00395438 | + | 0.999992i | \(0.498741\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.26543 | −0.558726 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.3964 | 1.64609 | 0.823046 | − | 0.567975i | \(-0.192273\pi\) | ||||
0.823046 | + | 0.567975i | \(0.192273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.344501 | 0.0206247 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9472 | −1.07064 | −0.535319 | − | 0.844650i | \(-0.679809\pi\) | ||||
−0.535319 | + | 0.844650i | \(0.679809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8925 | −1.18248 | −0.591242 | − | 0.806494i | \(-0.701362\pi\) | ||||
−0.591242 | + | 0.806494i | \(0.701362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0857046 | −0.00507670 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.19365 | 0.129038 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.04174 | −0.530036 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.76308 | −0.570365 | −0.285183 | − | 0.958473i | \(-0.592054\pi\) | ||||
−0.285183 | + | 0.958473i | \(0.592054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.32862 | −0.543133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.5013 | −1.30566 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.39750 | 0.0808193 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.4358 | 0.829313 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.6530 | 1.18259 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.571400 | −0.0326115 | −0.0163058 | − | 0.999867i | \(-0.505191\pi\) | ||||
−0.0163058 | + | 0.999867i | \(0.505191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.6311 | −1.40122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.6256 | −1.05616 | −0.528080 | − | 0.849195i | \(-0.677088\pi\) | ||||
−0.528080 | + | 0.849195i | \(0.677088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.6875 | −1.62152 | −0.810758 | − | 0.585382i | \(-0.800945\pi\) | ||||
−0.810758 | + | 0.585382i | \(0.800945\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5125 | 0.815101 | 0.407551 | − | 0.913183i | \(-0.366383\pi\) | ||||
0.407551 | + | 0.913183i | \(0.366383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.32862 | 0.522302 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.81896 | 0.436412 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.160152 | −0.00891110 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.75401 | −0.319175 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8413 | −0.599527 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4522 | −1.06919 | −0.534596 | − | 0.845108i | \(-0.679536\pi\) | ||||
−0.534596 | + | 0.845108i | \(0.679536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65947 | 0.0909383 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.1705 | −1.26594 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.6956 | −1.12736 | −0.563681 | − | 0.825993i | \(-0.690615\pi\) | ||||
−0.563681 | + | 0.825993i | \(0.690615\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.51949 | −0.136840 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.45456 | −0.0787687 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32596 | −0.0713870 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.83712 | 0.367036 | 0.183518 | − | 0.983016i | \(-0.441251\pi\) | ||||
0.183518 | + | 0.983016i | \(0.441251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.72280 | −0.306335 | −0.153167 | − | 0.988200i | \(-0.548947\pi\) | ||||
−0.153167 | + | 0.988200i | \(0.548947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.9738 | −0.745864 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2493 | −0.598738 | −0.299369 | − | 0.954137i | \(-0.596776\pi\) | ||||
−0.299369 | + | 0.954137i | \(0.596776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6058 | −0.615973 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.601190 | −0.0317296 | −0.0158648 | − | 0.999874i | \(-0.505050\pi\) | ||||
−0.0158648 | + | 0.999874i | \(0.505050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9987 | −0.999930 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.93112 | 0.363790 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.57721 | −0.448951 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.1077 | −1.10181 | −0.550907 | − | 0.834566i | \(-0.685718\pi\) | ||||
−0.550907 | + | 0.834566i | \(0.685718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.942381 | 0.0490584 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.8297 | −1.38919 | −0.694593 | − | 0.719403i | \(-0.744416\pi\) | ||||
−0.694593 | + | 0.719403i | \(0.744416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.1820 | 0.887272 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.79325 | 0.298368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6585 | −0.650225 | −0.325112 | − | 0.945675i | \(-0.605402\pi\) | ||||
−0.325112 | + | 0.945675i | \(0.605402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.48116 | 0.229577 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.49545 | −0.331902 | −0.165951 | − | 0.986134i | \(-0.553069\pi\) | ||||
−0.165951 | + | 0.986134i | \(0.553069\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.24386 | 0.114062 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.3163 | −0.928673 | −0.464337 | − | 0.885659i | \(-0.653707\pi\) | ||||
−0.464337 | + | 0.885659i | \(0.653707\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.47775 | −0.125305 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1342 | −0.662531 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.50913 | −0.176564 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.71680 | −0.286918 | −0.143459 | − | 0.989656i | \(-0.545822\pi\) | ||||
−0.143459 | + | 0.989656i | \(0.545822\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6987 | 0.534268 | 0.267134 | − | 0.963659i | \(-0.413923\pi\) | ||||
0.267134 | + | 0.963659i | \(0.413923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.903308 | −0.0449970 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.63763 | 0.429207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.00663 | −0.347306 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9005 | 1.62683 | 0.813413 | − | 0.581686i | \(-0.197607\pi\) | ||||
0.813413 | + | 0.581686i | \(0.197607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.8150 | −1.27336 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.4124 | 1.05109 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.5799 | −0.909860 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.12676 | 0.348165 | 0.174083 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174083 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.3900 | 0.798798 | 0.399399 | − | 0.916777i | \(-0.369219\pi\) | ||||
0.399399 | + | 0.916777i | \(0.369219\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.5514 | 0.610270 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.2018 | 0.494861 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.1033 | 0.680915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.33942 | −0.0645174 | −0.0322587 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322587 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.72105 | −0.467164 | −0.233582 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233582 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.49668 | −0.263546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0206744 | 0.000988989 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6772 | −0.652775 | −0.326388 | − | 0.945236i | \(-0.605831\pi\) | ||||
−0.326388 | + | 0.945236i | \(0.605831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4616 | 1.30474 | 0.652370 | − | 0.757901i | \(-0.273775\pi\) | ||||
0.652370 | + | 0.757901i | \(0.273775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.17499 | −0.103104 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.9467 | 1.03804 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.08587 | 0.381596 | 0.190798 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190798 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.97894 | −0.187361 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.2635 | −1.37492 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.72831 | −0.361515 | −0.180758 | − | 0.983528i | \(-0.557855\pi\) | ||||
−0.180758 | + | 0.983528i | \(0.557855\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.7754 | 1.15641 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8351 | −0.551214 | −0.275607 | − | 0.961270i | \(-0.588879\pi\) | ||||
−0.275607 | + | 0.961270i | \(0.588879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0041 | −0.464931 | −0.232465 | − | 0.972605i | \(-0.574679\pi\) | ||||
−0.232465 | + | 0.972605i | \(0.574679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.857065 | 0.0397455 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.8158 | 1.65736 | 0.828679 | − | 0.559724i | \(-0.189093\pi\) | ||||
0.828679 | + | 0.559724i | \(0.189093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4995 | 0.668101 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.47407 | −0.435618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0851241 | −0.00390576 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.54026 | 0.0705237 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.2210 | 0.923919 | 0.461960 | − | 0.886901i | \(-0.347146\pi\) | ||||
0.461960 | + | 0.886901i | \(0.347146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.35125 | −0.198400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3024 | 0.467807 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.12743 | −0.0510889 | −0.0255445 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255445 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.08318 | −0.139426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.3557 | −1.27968 | −0.639838 | − | 0.768510i | \(-0.720998\pi\) | ||||
−0.639838 | + | 0.768510i | \(0.720998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2714 | −0.462600 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.12860 | 0.275460 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.4975 | 0.783296 | 0.391648 | − | 0.920115i | \(-0.371905\pi\) | ||||
0.391648 | + | 0.920115i | \(0.371905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.95216 | 0.0872159 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.12359 | 0.228450 | 0.114225 | − | 0.993455i | \(-0.463562\pi\) | ||||
0.114225 | + | 0.993455i | \(0.463562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.4485 | −0.731947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.88929 | −0.439199 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.99019 | 0.176862 | 0.0884311 | − | 0.996082i | \(-0.471815\pi\) | ||||
0.0884311 | + | 0.996082i | \(0.471815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.206726 | −0.00912717 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.0653 | 1.23671 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.9947 | −2.33070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.5573 | 0.638997 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7251 | 0.864174 | 0.432087 | − | 0.901832i | \(-0.357777\pi\) | ||||
0.432087 | + | 0.901832i | \(0.357777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.7789 | −0.908599 | −0.454299 | − | 0.890849i | \(-0.650110\pi\) | ||||
−0.454299 | + | 0.890849i | \(0.650110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.60156 | 0.0697649 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6801 | −0.986093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.37868 | −0.233415 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47100 | −0.107031 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.90911 | −0.385175 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.3108 | −0.444946 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6710 | 0.931708 | 0.465854 | − | 0.884862i | \(-0.345747\pi\) | ||||
0.465854 | + | 0.884862i | \(0.345747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.3984 | −0.489152 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.3529 | 0.529139 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.5206 | 1.68978 | 0.844890 | − | 0.534940i | \(-0.179666\pi\) | ||||
0.844890 | + | 0.534940i | \(0.179666\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9081 | 0.508225 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0857046 | 0.00365114 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.12850 | 0.175245 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7066 | 0.792625 | 0.396313 | − | 0.918116i | \(-0.370290\pi\) | ||||
0.396313 | + | 0.918116i | \(0.370290\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.88358 | −0.248849 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.0051 | −1.05572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.29853 | 0.391886 | 0.195943 | − | 0.980615i | \(-0.437223\pi\) | ||||
0.195943 | + | 0.980615i | \(0.437223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.87077 | 0.120774 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7314 | −0.911028 | −0.455514 | − | 0.890229i | \(-0.650545\pi\) | ||||
−0.455514 | + | 0.890229i | \(0.650545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3218 | 0.766745 | 0.383373 | − | 0.923594i | \(-0.374762\pi\) | ||||
0.383373 | + | 0.923594i | \(0.374762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.8986 | −1.33258 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.31697 | −0.0549216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.722827 | −0.0300917 | −0.0150458 | − | 0.999887i | \(-0.504789\pi\) | ||||
−0.0150458 | + | 0.999887i | \(0.504789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.8087 | 0.532311 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.50332 | −0.269340 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.80598 | 0.157358 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.7638 | 1.35231 | 0.676153 | − | 0.736761i | \(-0.263646\pi\) | ||||
0.676153 | + | 0.736761i | \(0.263646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0133634 | −0.000550630 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.9147 | 0.572374 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.6267 | 0.559580 | 0.279790 | − | 0.960061i | \(-0.409735\pi\) | ||||
0.279790 | + | 0.960061i | \(0.409735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0640 | 0.575600 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.02869 | −0.205467 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4794 | 0.916953 | 0.458477 | − | 0.888706i | \(-0.348395\pi\) | ||||
0.458477 | + | 0.888706i | \(0.348395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3596 | −0.544045 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.89749 | −0.321079 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9787 | 1.33856 | 0.669282 | − | 0.743009i | \(-0.266602\pi\) | ||||
0.669282 | + | 0.743009i | \(0.266602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.9107 | −1.33143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7081 | 0.997951 | 0.498976 | − | 0.866616i | \(-0.333710\pi\) | ||||
0.498976 | + | 0.866616i | \(0.333710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.34450 | 0.0945394 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7493 | 0.915852 | 0.457926 | − | 0.888990i | \(-0.348593\pi\) | ||||
0.457926 | + | 0.888990i | \(0.348593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.90664 | 0.317795 | 0.158897 | − | 0.987295i | \(-0.449206\pi\) | ||||
0.158897 | + | 0.987295i | \(0.449206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.19830 | −0.128343 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.93443 | −0.317377 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.208643 | 0.00833239 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.71474 | 0.307607 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0800 | −1.31689 | −0.658447 | − | 0.752627i | \(-0.728786\pi\) | ||||
−0.658447 | + | 0.752627i | \(0.728786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.4380 | −0.931576 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.10594 | −0.202623 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.69167 | −0.264718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.9032 | −1.02311 | −0.511557 | − | 0.859250i | \(-0.670931\pi\) | ||||
−0.511557 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.69377 | −0.263977 | −0.131988 | − | 0.991251i | \(-0.542136\pi\) | ||||
−0.131988 | + | 0.991251i | \(0.542136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.58239 | 0.219806 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.44119 | −0.371172 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7100 | 0.891444 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.3525 | 1.65738 | 0.828691 | − | 0.559706i | \(-0.189086\pi\) | ||||
0.828691 | + | 0.559706i | \(0.189086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.9654 | 0.584746 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.94543 | −0.192940 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.166508 | 0.00648622 | 0.00324311 | − | 0.999995i | \(-0.498968\pi\) | ||||
0.00324311 | + | 0.999995i | \(0.498968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0731 | −0.702963 | −0.351481 | − | 0.936195i | \(-0.614322\pi\) | ||||
−0.351481 | + | 0.936195i | \(0.614322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.5286 | −0.603082 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.32596 | 0.0513412 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.3429 | 0.941151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.2785 | −1.94098 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.6060 | −1.06413 | −0.532067 | − | 0.846702i | \(-0.678584\pi\) | ||||
−0.532067 | + | 0.846702i | \(0.678584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.1686 | 0.506860 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.03680 | −0.116714 | −0.0583569 | − | 0.998296i | \(-0.518586\pi\) | ||||
−0.0583569 | + | 0.998296i | \(0.518586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.3952 | 1.31803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.28916 | −0.278912 | −0.139456 | − | 0.990228i | \(-0.544535\pi\) | ||||
−0.139456 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.4142 | 1.12386 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.28315 | 0.277870 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.03868 | −0.153862 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.41348 | 0.167897 | 0.0839483 | − | 0.996470i | \(-0.473247\pi\) | ||||
0.0839483 | + | 0.996470i | \(0.473247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.1703 | 0.803037 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.38106 | 0.165944 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.5421 | −0.663505 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.55509 | −0.360891 | −0.180445 | − | 0.983585i | \(-0.557754\pi\) | ||||
−0.180445 | + | 0.983585i | \(0.557754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0643719 | −0.00242783 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.2260 | 1.17604 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8291 | 0.932477 | 0.466239 | − | 0.884659i | \(-0.345609\pi\) | ||||
0.466239 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.02329 | −0.0758794 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.206748 | −0.00774279 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0697 | −0.600972 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5263 | −0.915950 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7345 | −1.22079 | −0.610395 | − | 0.792097i | \(-0.708989\pi\) | ||||
−0.610395 | + | 0.792097i | \(0.708989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.48288 | −0.352672 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.45945 | −0.202759 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7398 | −0.657932 | −0.328966 | − | 0.944342i | \(-0.606700\pi\) | ||||
−0.328966 | + | 0.944342i | \(0.606700\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.3160 | 1.08578 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4315 | 0.385825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.5257 | 0.499582 | 0.249791 | − | 0.968300i | \(-0.419638\pi\) | ||||
0.249791 | + | 0.968300i | \(0.419638\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56.4071 | 2.07778 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.3968 | 0.639952 | 0.319976 | − | 0.947426i | \(-0.396325\pi\) | ||||
0.319976 | + | 0.947426i | \(0.396325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.129571 | 0.00475992 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.79349 | −0.285915 | −0.142958 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142958 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.0066 | −0.916172 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.3460 | 0.451715 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0634 | 0.878087 | 0.439043 | − | 0.898466i | \(-0.355317\pi\) | ||||
0.439043 | + | 0.898466i | \(0.355317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.8294 | −0.759066 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3436 | 1.21350 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.9399 | 1.77875 | 0.889376 | − | 0.457177i | \(-0.151140\pi\) | ||||
0.889376 | + | 0.457177i | \(0.151140\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.22796 | 0.117167 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3401 | 0.991079 | 0.495540 | − | 0.868585i | \(-0.334970\pi\) | ||||
0.495540 | + | 0.868585i | \(0.334970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.74797 | −0.243973 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.1033 | 0.509242 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.9324 | −0.754842 | −0.377421 | − | 0.926042i | \(-0.623189\pi\) | ||||
−0.377421 | + | 0.926042i | \(0.623189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.42671 | 0.195438 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.7545 | 1.68164 | 0.840822 | − | 0.541312i | \(-0.182072\pi\) | ||||
0.840822 | + | 0.541312i | \(0.182072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.851260 | 0.0305782 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0365556 | −0.00130974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.2537 | 1.01100 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.2584 | −0.473817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5211 | −0.589662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.76023 | 0.205330 | 0.102665 | − | 0.994716i | \(-0.467263\pi\) | ||||
0.102665 | + | 0.994716i | \(0.467263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.7732 | −1.55837 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.2239 | −1.10879 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.83194 | 0.135905 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.6110 | 0.871766 | 0.435883 | − | 0.900003i | \(-0.356436\pi\) | ||||
0.435883 | + | 0.900003i | \(0.356436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.3505 | 2.06429 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.25405 | −0.0443097 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.8807 | 0.736864 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.80409 | 0.204314 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.9653 | −1.08868 | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||||
−0.544341 | + | 0.838864i | \(0.683220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.3652 | −1.66322 | −0.831609 | − | 0.555362i | \(-0.812580\pi\) | ||||
−0.831609 | + | 0.555362i | \(0.812580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.186756 | 0.00654983 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.51305 | 0.123057 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0870409 | −0.00304518 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.09335 | −0.0381582 | −0.0190791 | − | 0.999818i | \(-0.506073\pi\) | ||||
−0.0190791 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.9949 | 1.18499 | 0.592493 | − | 0.805575i | \(-0.298144\pi\) | ||||
0.592493 | + | 0.805575i | \(0.298144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.2907 | −0.462723 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.5948 | 0.577059 | 0.288529 | − | 0.957471i | \(-0.406834\pi\) | ||||
0.288529 | + | 0.957471i | \(0.406834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.51910 | 0.0527605 | 0.0263803 | − | 0.999652i | \(-0.491602\pi\) | ||||
0.0263803 | + | 0.999652i | \(0.491602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.2985 | 1.36325 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.22433 | −0.0769762 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.06731 | 0.0714565 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.9564 | 1.44849 | 0.724247 | − | 0.689541i | \(-0.242188\pi\) | ||||
0.724247 | + | 0.689541i | \(0.242188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5033 | −0.810459 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.7442 | −0.886676 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.2681 | 0.387634 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5345 | −0.979303 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.995912 | −0.0341394 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6644 | −1.08417 | −0.542084 | − | 0.840324i | \(-0.682365\pi\) | ||||
−0.542084 | + | 0.840324i | \(0.682365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0563052 | 0.00192560 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.4789 | 1.55353 | 0.776764 | − | 0.629792i | \(-0.216860\pi\) | ||||
0.776764 | + | 0.629792i | \(0.216860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2872 | 0.726309 | 0.363154 | − | 0.931729i | \(-0.381700\pi\) | ||||
0.363154 | + | 0.931729i | \(0.381700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.77970 | 0.162703 | 0.0813514 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813514 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.5870 | −0.563975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.14667 | 0.106866 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.54278 | 0.289794 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.0299 | 1.18694 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.94013 | 0.201043 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.9215 | −1.68573 | −0.842864 | − | 0.538126i | \(-0.819132\pi\) | ||||
−0.842864 | + | 0.538126i | \(0.819132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0046 | −0.472362 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.69012 | −0.225396 | −0.112698 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112698 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3012 | −1.32259 | −0.661295 | − | 0.750125i | \(-0.729993\pi\) | ||||
−0.661295 | + | 0.750125i | \(0.729993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.3813 | −0.449809 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.5777 | −1.76539 | −0.882693 | − | 0.469950i | \(-0.844272\pi\) | ||||
−0.882693 | + | 0.469950i | \(0.844272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0278 | −0.704457 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.486877 | −0.0162927 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7484 | 0.392706 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.00462 | 0.0669325 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.857065 | −0.0285847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.16056 | 0.238553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.9876 | 0.431722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3793 | 1.04193 | 0.520967 | − | 0.853577i | \(-0.325571\pi\) | ||||
0.520967 | + | 0.853577i | \(0.325571\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.48383 | −0.314559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.20500 | 0.172449 | 0.0862247 | − | 0.996276i | \(-0.472520\pi\) | ||||
0.0862247 | + | 0.996276i | \(0.472520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.1273 | −1.72516 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.6255 | 0.979390 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.7249 | −0.815599 | −0.407799 | − | 0.913072i | \(-0.633704\pi\) | ||||
−0.407799 | + | 0.913072i | \(0.633704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.819640 | −0.0270080 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.5461 | 0.577536 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.10054 | 0.134825 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.1819 | 0.531482 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.1957 | −1.77810 | −0.889051 | − | 0.457808i | \(-0.848635\pi\) | ||||
−0.889051 | + | 0.457808i | \(0.848635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.7173 | −0.874684 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.4914 | 0.931768 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.7937 | 0.809974 | 0.404987 | − | 0.914323i | \(-0.367276\pi\) | ||||
0.404987 | + | 0.914323i | \(0.367276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.1506 | −1.34290 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9574 | 0.520198 | 0.260099 | − | 0.965582i | \(-0.416245\pi\) | ||||
0.260099 | + | 0.965582i | \(0.416245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.565560 | −0.0184172 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.9098 | −0.776965 | −0.388482 | − | 0.921456i | \(-0.627001\pi\) | ||||
−0.388482 | + | 0.921456i | \(0.627001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9673 | 0.420937 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.8173 | 0.675046 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.6927 | 1.80406 | 0.902032 | − | 0.431668i | \(-0.142075\pi\) | ||||
0.902032 | + | 0.431668i | \(0.142075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.3460 | 1.17613 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.3813 | 0.432558 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8664 | −0.995689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.13681 | −0.165531 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.5945 | −0.469815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.1200 | 0.550541 | 0.275271 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275271 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.229729 | −0.00737995 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2317 | 0.392534 | 0.196267 | − | 0.980551i | \(-0.437118\pi\) | ||||
0.196267 | + | 0.980551i | \(0.437118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.25378 | −0.264333 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.6047 | −1.55500 | −0.777500 | − | 0.628883i | \(-0.783513\pi\) | ||||
−0.777500 | + | 0.628883i | \(0.783513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.29487 | 0.169225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.12240 | 0.227401 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.39481 | −0.0444875 | −0.0222437 | − | 0.999753i | \(-0.507081\pi\) | ||||
−0.0222437 | + | 0.999753i | \(0.507081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.8547 | −0.505174 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.34663 | −0.0428203 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.13504 | 0.163120 | 0.0815600 | − | 0.996668i | \(-0.474010\pi\) | ||||
0.0815600 | + | 0.996668i | \(0.474010\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.9031 | −0.885477 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0248 | −0.508022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6680 | 0.781244 | 0.390622 | − | 0.920551i | \(-0.372260\pi\) | ||||
0.390622 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.95826 | 0.315065 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8036.2.a.j.1.4 | 5 | ||
7.6 | odd | 2 | 1148.2.a.e.1.2 | ✓ | 5 | ||
28.27 | even | 2 | 4592.2.a.bd.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.e.1.2 | ✓ | 5 | 7.6 | odd | 2 | ||
4592.2.a.bd.1.4 | 5 | 28.27 | even | 2 | |||
8036.2.a.j.1.4 | 5 | 1.1 | even | 1 | trivial |